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vovangra [49]
2 years ago
10

Rachael’s employer matches 16% of Rachel’s contribution to her 401k plan. If racheals employer contributed $400 to the plan a ye

ar , how much did racheal contribute to the plan last year
Mathematics
2 answers:
Butoxors [25]2 years ago
4 0
If x is Rachael's contributions
400=16%x
2,500=x

Rachael contributed $2,500 to her 401k last year
olga2289 [7]2 years ago
3 0

Answer:

$2500.

Step-by-step explanation:

Let x be represent the amount contributed by Rachael's to her 401(k) plan.

We have been given that Rachael’s employer matches 16% of Rachel’s contribution to her 401(k) plan. Rachael's employer contributed $400 to the plan a year.

We need to find x such that 16% of x is $400.

\frac{16}{100}*x=\$400

0.16*x=\$400

\frac{0.16*x}{0.16}=\frac{\$400}{0.16}

x=\$2500

Therefore, Rachael contributed $2500 to the plan last year.

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Solve the given initial value problem and determine how the interval in which the solution exists depends on the initial value y
zalisa [80]

Answer:

y has a finite solution for any value y_0 ≠ 0.

Step-by-step explanation:

Given the differential equation

y' + y³ = 0

We can rewrite this as

dy/dx + y³ = 0

Multiplying through by dx

dy + y³dx = 0

Divide through by y³, we have

dy/y³ + dx = 0

dy/y³ = -dx

Integrating both sides

-1/(2y²) = - x + c

Multiplying through by -1, we have

1/(2y²) = x + C (Where C = -c)

Applying the initial condition y(0) = y_0, put x = 0, and y = y_0

1/(2y_0²) = 0 + C

C = 1/(2y_0²)

So

1/(2y²) = x + 1/(2y_0²)

2y² = 1/[x + 1/(2y_0²)]

y² = 1/[2x + 1/(y_0²)]

y = 1/[2x + 1/(y_0²)]½

This is the required solution to the initial value problem.

The interval of the solution depends on the value of y_0. There are infinitely many solutions for y_0 assumes a real number.

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With this, y has a finite solution for any value y_0 ≠ 0.

8 0
2 years ago
a scientist wants to study 24 stars he studies 1/3 of them one week and 1/4 of them next week how many of them are left to study
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Work this travel problem based on the data provided in the various tables in this section.
grigory [225]
42% ................................
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2 years ago
On her first day in a hospital, Kiri receives u1 milligrams (mg) of a therapeutic drug. The amount of the drug Kiri receives inc
Valentin [98]

Answer:

a. 21 = u1 + 6·d

b. 29 = u1 + 10·d

c. d = 2, u1 = 9

Step-by-step explanation:

a. The given parameters are;

The amount of therapeutic drug Kiri receives on her first at the hospital = u1 milligrams

The amount of drug increase received by Kiri each day = d

The amount of drug Kiri received on the seventh day = 21 mg

The amount of drug she received on the eleventh day = 29 mg

Therefore, we have an arithmetic progression with the formula for the nth term given as follows;

aₙ = a₁ + (n - 1)·d

Where;

a₁ = u1

n = The number of terms

Therefore, for the 7th day, the amount of drugs she receives, which is 21 milligrams, is given as follows;

a₇ = u1 + (7 - 1)·d = u1 + 6·d = 21

The equation for the amount of drugs she receives in terms of u1 and d on the seventh day is given as follows;

21 = u1 + 6·d

b. For the eleventh day, the amount of drugs she receives, which is 29 milligrams, is given as follows;

a₁₁ = u1 + (11 - 1)·d = u1 + 10·d = 29

Therefore, the equation for the amount of drugs she receives in terms of u1 and d on the  eleventh day is given as follows;

29 = u1 + 10·d

c. Therefore, we have two equations which are given as follows;

21 = u1 + 6·d................(1)

29 = u1 + 10·d..............(2)

Subtracting equation (1) from equation (2) gives;

29 - 21 = (u1 + 10·d) - (u1 + 6·d)

8 = 4·d

d = 8/4 = 2

d = 2

From equation (1), we have;

21 = u1 + 6·d = u1 + 6×2 = u1 + 12

21 = u1 + 12

21 - 12 = u1

∴ u1 = 9

d = 2, u1 = 9.

4 0
1 year ago
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